The roots of the equation `|x^2-x-6|=x+2` are

Options

A. `-2,1,4`
B. `0,2,4`
C. `0,1,4`
D. `-2,2,4`

Answer

B

Explanation

Given , `|x^(2) - x- 6| = x+2 `
`:. X^(2) - x- 6 = x+2 and x^(2) - x- 6 = - (x+2)`
`rArr x^(2)-2x - 8 = 0 `
`rArr x^(2) - x- 6 = -x - 2 `
`rArr x^(2) - 4x + 2x - 8 = 0 `
`rArr x^(2) = 4`
`rArr x(x-4)+2(x-4) = 0 `
`rArr x= + 2, -2`
`rArr x=4,-2`
` :. x= -2, 2, 4.`